definition of function
Topics
About: set
The table of contents of this article
Starting Context
- The reader knows a definition of relation.
Target Context
- The reader will have a definition of function.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\(*F\): \(\in \{\text{ the relations }\}\)
//
Conditions:
\(\forall \langle s_1, s_2 \rangle, \langle s_1, s_3 \rangle \in F (s_2 = s_3)\)
//
2: Note
Conditions means that each element of the domain has the unique corresponding element in the range.
'map' is different from 'function' in this definition in that it has the codomain, which does not necessarily equal the range, although a map is often called "function".
